12n
0532
(K12n
0532
)
A knot diagram
1
Linearized knot diagam
3 5 10 12 2 11 4 5 7 3 9 8
Solving Sequence
3,5
2
6,11
7 1 10 4 9 8 12
c
2
c
5
c
6
c
1
c
10
c
3
c
9
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.61870 × 10
329
u
98
− 5.11065 × 10
328
u
97
+ ··· + 4.51920 × 10
331
b − 4.15006 × 10
331
,
3.15837 × 10
331
u
98
− 2.19273 × 10
330
u
97
+ ··· + 1.40095 × 10
333
a − 5.59957 × 10
333
,
u
99
+ 53u
97
+ ··· − 259u + 31i
I
u
2
= h−1.19415 × 10
16
u
36
− 1.97876 × 10
16
u
35
+ ··· + 3.72808 × 10
15
b + 1.06100 × 10
16
,
− 7.14844 × 10
15
u
36
− 9.64409 × 10
15
u
35
+ ··· + 3.72808 × 10
15
a − 3.18284 × 10
16
, u
37
+ u
36
+ ··· − 8u − 1i
* 2 irreducible components of dim
C
= 0, with total 136 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.62 × 10
329
u
98
− 5.11 × 10
328
u
97
+ · · · + 4.52 × 10
331
b − 4.15 ×
10
331
, 3.16 × 10
331
u
98
− 2.19 × 10
330
u
97
+ · · · + 1.40 × 10
333
a − 5.60 ×
10
333
, u
99
+ 53u
97
+ · · · − 259u + 31i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
11
=
−0.0225444u
98
+ 0.00156517u
97
+ ··· − 98.9674u + 3.99697
0.00358184u
98
+ 0.00113087u
97
+ ··· + 0.568838u + 0.918316
a
7
=
−0.0443461u
98
− 0.00855901u
97
+ ··· − 79.0333u + 1.08105
0.00402845u
98
+ 0.000590727u
97
+ ··· − 2.96656u + 0.894483
a
1
=
u
2
+ 1
u
2
a
10
=
−0.0189626u
98
+ 0.00269604u
97
+ ··· − 98.3986u + 4.91529
0.00358184u
98
+ 0.00113087u
97
+ ··· + 0.568838u + 0.918316
a
4
=
−0.0310245u
98
+ 0.00405756u
97
+ ··· − 96.3241u + 6.72622
−0.000256772u
98
− 0.000349871u
97
+ ··· − 3.51712u + 1.04145
a
9
=
−0.0829098u
98
− 0.00721519u
97
+ ··· − 145.839u − 1.52124
0.00219888u
98
+ 0.00435927u
97
+ ··· − 14.5292u + 2.33219
a
8
=
−0.0829098u
98
− 0.00721519u
97
+ ··· − 145.839u − 1.52124
0.000152831u
98
+ 0.00273447u
97
+ ··· − 15.2307u + 2.10852
a
12
=
0.0180850u
98
− 0.00679441u
97
+ ··· + 40.9484u − 14.4549
−0.00705979u
98
− 0.00186554u
97
+ ··· − 8.85440u + 0.261167
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0330848u
98
− 0.00300896u
97
+ ··· + 76.4947u + 7.16298
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
+ 106u
98
+ ··· − 170255u − 961
c
2
, c
5
u
99
+ 53u
97
+ ··· − 259u + 31
c
3
, c
10
u
99
+ 27u
97
+ ··· − 45156u + 28964
c
4
u
99
+ 3u
98
+ ··· + 29u + 1
c
6
u
99
− 8u
98
+ ··· + 11559416u + 409289
c
7
u
99
+ u
98
+ ··· + 263227u + 47969
c
8
u
99
+ 2u
98
+ ··· − 5274u − 59
c
9
u
99
− 9u
98
+ ··· − 402u − 215
c
11
u
99
− 6u
98
+ ··· − 12984u + 3173
c
12
u
99
− u
98
+ ··· + 11196996u + 1212452
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
− 198y
98
+ ··· − 1536870623y −923521
c
2
, c
5
y
99
+ 106y
98
+ ··· − 170255y −961
c
3
, c
10
y
99
+ 54y
98
+ ··· − 26392577344y −838913296
c
4
y
99
+ 21y
98
+ ··· + 287y −1
c
6
y
99
+ 14y
98
+ ··· + 14727329603844y −167517485521
c
7
y
99
− y
98
+ ··· + 66159723473y −2301024961
c
8
y
99
− 14y
98
+ ··· + 8482664y −3481
c
9
y
99
− 37y
98
+ ··· + 769624y −46225
c
11
y
99
− 20y
98
+ ··· − 584095766y −10067929
c
12
y
99
+ 5y
98
+ ··· + 5946396266144y −1470039852304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.449463 + 0.920420I
a = 0.380654 − 0.863384I
b = −0.287498 − 1.090140I
2.33708 − 5.55546I 0
u = −0.449463 − 0.920420I
a = 0.380654 + 0.863384I
b = −0.287498 + 1.090140I
2.33708 + 5.55546I 0
u = 0.989702 + 0.361143I
a = 0.723225 + 0.816298I
b = −0.593040 + 1.230230I
0.29355 + 4.78047I 0
u = 0.989702 − 0.361143I
a = 0.723225 − 0.816298I
b = −0.593040 − 1.230230I
0.29355 − 4.78047I 0
u = 0.776838 + 0.723144I
a = 0.163427 + 0.003710I
b = 0.453158 + 0.898313I
−0.964664 + 0.845567I 0
u = 0.776838 − 0.723144I
a = 0.163427 − 0.003710I
b = 0.453158 − 0.898313I
−0.964664 − 0.845567I 0
u = −0.884203 + 0.198301I
a = −0.172383 + 1.092170I
b = 0.473016 + 0.798138I
−1.27586 − 4.76408I 0
u = −0.884203 − 0.198301I
a = −0.172383 − 1.092170I
b = 0.473016 − 0.798138I
−1.27586 + 4.76408I 0
u = −0.074327 + 1.099590I
a = 0.28126 + 2.12391I
b = −0.400780 − 0.695484I
2.84341 + 2.27358I 0
u = −0.074327 − 1.099590I
a = 0.28126 − 2.12391I
b = −0.400780 + 0.695484I
2.84341 − 2.27358I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.100382 + 1.131240I
a = 0.15482 + 2.33675I
b = 0.336290 − 0.620402I
2.33767 + 5.94152I 0
u = 0.100382 − 1.131240I
a = 0.15482 − 2.33675I
b = 0.336290 + 0.620402I
2.33767 − 5.94152I 0
u = 0.007624 + 0.863581I
a = −0.71439 + 1.52331I
b = 0.170924 − 1.193600I
1.47026 + 4.79432I 0
u = 0.007624 − 0.863581I
a = −0.71439 − 1.52331I
b = 0.170924 + 1.193600I
1.47026 − 4.79432I 0
u = 0.924315 + 0.669384I
a = 0.453346 + 0.855141I
b = −0.816396 + 0.665074I
−0.0948162 + 0.0797592I 0
u = 0.924315 − 0.669384I
a = 0.453346 − 0.855141I
b = −0.816396 − 0.665074I
−0.0948162 − 0.0797592I 0
u = −0.669840 + 0.535577I
a = 1.151360 − 0.720481I
b = 0.103338 − 0.884220I
3.44466 + 1.11589I 0
u = −0.669840 − 0.535577I
a = 1.151360 + 0.720481I
b = 0.103338 + 0.884220I
3.44466 − 1.11589I 0
u = 0.602702 + 0.978790I
a = −0.689533 + 0.399947I
b = −0.087589 − 0.819332I
1.50660 + 3.93239I 0
u = 0.602702 − 0.978790I
a = −0.689533 − 0.399947I
b = −0.087589 + 0.819332I
1.50660 − 3.93239I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.901703 + 0.736467I
a = −0.0451128 + 0.0657810I
b = 1.009140 + 0.461921I
−0.34961 + 6.23060I 0
u = 0.901703 − 0.736467I
a = −0.0451128 − 0.0657810I
b = 1.009140 − 0.461921I
−0.34961 − 6.23060I 0
u = 0.745265 + 0.362689I
a = 0.000194 − 0.396282I
b = 0.464260 − 0.826650I
3.34931 + 1.03766I 0
u = 0.745265 − 0.362689I
a = 0.000194 + 0.396282I
b = 0.464260 + 0.826650I
3.34931 − 1.03766I 0
u = 0.095723 + 0.821995I
a = 1.192920 + 0.548778I
b = 0.061204 − 1.279230I
5.13444 + 0.35658I 0
u = 0.095723 − 0.821995I
a = 1.192920 − 0.548778I
b = 0.061204 + 1.279230I
5.13444 − 0.35658I 0
u = −0.856107 + 0.834764I
a = 0.517321 − 0.351198I
b = −0.093212 − 0.986432I
5.74308 − 3.12727I 0
u = −0.856107 − 0.834764I
a = 0.517321 + 0.351198I
b = −0.093212 + 0.986432I
5.74308 + 3.12727I 0
u = 0.092174 + 0.789815I
a = −0.018180 + 0.859448I
b = 0.243265 − 1.352150I
5.46584 + 4.99973I 0
u = 0.092174 − 0.789815I
a = −0.018180 − 0.859448I
b = 0.243265 + 1.352150I
5.46584 − 4.99973I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110540 + 0.511836I
a = −0.586814 + 0.687680I
b = 0.689492 + 1.188880I
1.94491 − 12.39280I 0
u = −1.110540 − 0.511836I
a = −0.586814 − 0.687680I
b = 0.689492 − 1.188880I
1.94491 + 12.39280I 0
u = −0.564604 + 0.483711I
a = 0.183144 − 0.072820I
b = −0.915705 + 0.256094I
−2.66072 + 0.68787I 0
u = −0.564604 − 0.483711I
a = 0.183144 + 0.072820I
b = −0.915705 − 0.256094I
−2.66072 − 0.68787I 0
u = 0.965432 + 0.809020I
a = −0.284876 − 0.157684I
b = 0.174022 − 0.782029I
4.96132 + 3.43570I 0
u = 0.965432 − 0.809020I
a = −0.284876 + 0.157684I
b = 0.174022 + 0.782029I
4.96132 − 3.43570I 0
u = −0.016021 + 0.727396I
a = 0.744128 + 0.572179I
b = −0.20015 − 1.40684I
5.66046 − 4.73411I 7.47226 + 7.54887I
u = −0.016021 − 0.727396I
a = 0.744128 − 0.572179I
b = −0.20015 + 1.40684I
5.66046 + 4.73411I 7.47226 − 7.54887I
u = −0.885265 + 0.922396I
a = 0.93169 − 1.63224I
b = −0.09307 − 1.62375I
8.02930 − 3.25944I 0
u = −0.885265 − 0.922396I
a = 0.93169 + 1.63224I
b = −0.09307 + 1.62375I
8.02930 + 3.25944I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234061 + 0.612799I
a = 0.285773 − 0.530930I
b = −0.407982 − 1.268020I
2.19138 − 5.42561I −2.53703 + 9.57555I
u = −0.234061 − 0.612799I
a = 0.285773 + 0.530930I
b = −0.407982 + 1.268020I
2.19138 + 5.42561I −2.53703 − 9.57555I
u = −0.954291 + 0.953963I
a = −0.0892329 + 0.0111021I
b = −0.669835 + 0.942203I
0.69700 + 5.44894I 0
u = −0.954291 − 0.953963I
a = −0.0892329 − 0.0111021I
b = −0.669835 − 0.942203I
0.69700 − 5.44894I 0
u = 0.344285 + 0.509140I
a = 0.614615 + 0.516455I
b = −0.240304 + 0.507083I
−0.010371 + 1.152960I −0.45734 − 5.72489I
u = 0.344285 − 0.509140I
a = 0.614615 − 0.516455I
b = −0.240304 − 0.507083I
−0.010371 − 1.152960I −0.45734 + 5.72489I
u = 0.10854 + 1.45535I
a = 1.386540 + 0.042187I
b = −0.908690 + 0.807044I
−3.81992 − 0.72093I 0
u = 0.10854 − 1.45535I
a = 1.386540 − 0.042187I
b = −0.908690 − 0.807044I
−3.81992 + 0.72093I 0
u = −0.10960 + 1.46424I
a = −1.84124 + 0.02145I
b = 1.55189 + 0.62097I
−7.91560 − 1.49599I 0
u = −0.10960 − 1.46424I
a = −1.84124 − 0.02145I
b = 1.55189 − 0.62097I
−7.91560 + 1.49599I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15530 + 1.47142I
a = −1.198180 + 0.213225I
b = 0.426419 + 0.517451I
−5.23087 + 1.77261I 0
u = −0.15530 − 1.47142I
a = −1.198180 − 0.213225I
b = 0.426419 − 0.517451I
−5.23087 − 1.77261I 0
u = −0.02559 + 1.47939I
a = 0.197837 − 0.543845I
b = −0.13512 + 1.81976I
−0.49001 − 3.57941I 0
u = −0.02559 − 1.47939I
a = 0.197837 + 0.543845I
b = −0.13512 − 1.81976I
−0.49001 + 3.57941I 0
u = 0.129823 + 0.501429I
a = 1.306120 + 0.239520I
b = −0.608170 + 0.458382I
−0.12758 + 2.03530I −3.94463 − 5.13845I
u = 0.129823 − 0.501429I
a = 1.306120 − 0.239520I
b = −0.608170 − 0.458382I
−0.12758 − 2.03530I −3.94463 + 5.13845I
u = 0.06552 + 1.50863I
a = 1.330260 + 0.045882I
b = −0.579457 + 1.015220I
−6.74620 − 1.98513I 0
u = 0.06552 − 1.50863I
a = 1.330260 − 0.045882I
b = −0.579457 − 1.015220I
−6.74620 + 1.98513I 0
u = 0.15031 + 1.50678I
a = 1.335870 − 0.314116I
b = −1.06177 + 1.05023I
−2.85225 + 3.92690I 0
u = 0.15031 − 1.50678I
a = 1.335870 + 0.314116I
b = −1.06177 − 1.05023I
−2.85225 − 3.92690I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29344 + 1.51721I
a = −1.293750 − 0.102136I
b = 0.656632 − 1.048550I
−7.22483 + 4.07577I 0
u = 0.29344 − 1.51721I
a = −1.293750 + 0.102136I
b = 0.656632 + 1.048550I
−7.22483 − 4.07577I 0
u = 0.09950 + 1.54213I
a = −1.44627 + 0.26452I
b = 0.854251 − 0.847301I
−6.87766 + 3.21394I 0
u = 0.09950 − 1.54213I
a = −1.44627 − 0.26452I
b = 0.854251 + 0.847301I
−6.87766 − 3.21394I 0
u = −0.42150 + 1.49357I
a = 1.153460 − 0.212027I
b = −0.562638 − 1.165240I
−6.71949 − 9.70184I 0
u = −0.42150 − 1.49357I
a = 1.153460 + 0.212027I
b = −0.562638 + 1.165240I
−6.71949 + 9.70184I 0
u = −0.09642 + 1.55493I
a = −1.249440 − 0.615146I
b = 0.88571 + 1.37991I
−5.07786 − 6.90046I 0
u = −0.09642 − 1.55493I
a = −1.249440 + 0.615146I
b = 0.88571 − 1.37991I
−5.07786 + 6.90046I 0
u = 0.01774 + 1.58324I
a = −0.569305 + 0.524028I
b = 0.18170 + 1.41637I
−2.16703 − 4.61474I 0
u = 0.01774 − 1.58324I
a = −0.569305 − 0.524028I
b = 0.18170 − 1.41637I
−2.16703 + 4.61474I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11523 + 1.58503I
a = −1.258050 − 0.232343I
b = 0.344246 + 0.941272I
−3.94420 − 1.39890I 0
u = −0.11523 − 1.58503I
a = −1.258050 + 0.232343I
b = 0.344246 − 0.941272I
−3.94420 + 1.39890I 0
u = −0.26660 + 1.56711I
a = −1.225090 + 0.523394I
b = 1.39876 − 0.31492I
−9.32625 − 2.79394I 0
u = −0.26660 − 1.56711I
a = −1.225090 − 0.523394I
b = 1.39876 + 0.31492I
−9.32625 + 2.79394I 0
u = 0.16827 + 1.59853I
a = 1.106590 − 0.431611I
b = −0.805158 + 0.968421I
−3.29792 + 7.02458I 0
u = 0.16827 − 1.59853I
a = 1.106590 + 0.431611I
b = −0.805158 − 0.968421I
−3.29792 − 7.02458I 0
u = 0.42078 + 1.55266I
a = −1.50413 − 0.03210I
b = 0.71068 − 1.37025I
−5.84524 + 10.03770I 0
u = 0.42078 − 1.55266I
a = −1.50413 + 0.03210I
b = 0.71068 + 1.37025I
−5.84524 − 10.03770I 0
u = 0.122026 + 0.366129I
a = 3.37423 − 4.46100I
b = −0.291352 − 1.174280I
4.86450 − 5.17783I 9.36120 + 6.43156I
u = 0.122026 − 0.366129I
a = 3.37423 + 4.46100I
b = −0.291352 + 1.174280I
4.86450 + 5.17783I 9.36120 − 6.43156I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11601 + 1.61062I
a = −1.092310 − 0.514662I
b = 0.554317 + 1.164830I
−2.89782 − 5.94500I 0
u = −0.11601 − 1.61062I
a = −1.092310 + 0.514662I
b = 0.554317 − 1.164830I
−2.89782 + 5.94500I 0
u = 0.24750 + 1.63553I
a = 1.205180 + 0.393283I
b = −1.41575 − 0.32390I
−8.31396 + 10.41990I 0
u = 0.24750 − 1.63553I
a = 1.205180 − 0.393283I
b = −1.41575 + 0.32390I
−8.31396 − 10.41990I 0
u = 0.10452 + 1.65273I
a = 1.115920 − 0.696101I
b = −0.413837 + 0.798020I
−7.63047 + 6.05503I 0
u = 0.10452 − 1.65273I
a = 1.115920 + 0.696101I
b = −0.413837 − 0.798020I
−7.63047 − 6.05503I 0
u = −0.40356 + 1.60685I
a = 1.411000 + 0.036399I
b = −0.75772 − 1.38230I
−4.8993 − 17.9291I 0
u = −0.40356 − 1.60685I
a = 1.411000 − 0.036399I
b = −0.75772 + 1.38230I
−4.8993 + 17.9291I 0
u = 0.22703 + 1.66260I
a = 0.668359 + 0.230859I
b = −0.692357 − 0.412144I
−9.05435 + 4.80057I 0
u = 0.22703 − 1.66260I
a = 0.668359 − 0.230859I
b = −0.692357 + 0.412144I
−9.05435 − 4.80057I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15035 + 1.67413I
a = −0.841817 + 0.262191I
b = 0.866086 − 0.528143I
−8.78633 + 1.54908I 0
u = −0.15035 − 1.67413I
a = −0.841817 − 0.262191I
b = 0.866086 + 0.528143I
−8.78633 − 1.54908I 0
u = −0.129576 + 0.278011I
a = −2.76297 − 3.97519I
b = 0.273923 − 1.343870I
5.51201 − 2.99398I 8.78954 + 4.65677I
u = −0.129576 − 0.278011I
a = −2.76297 + 3.97519I
b = 0.273923 + 1.343870I
5.51201 + 2.99398I 8.78954 − 4.65677I
u = −0.303524
a = −1.02169
b = −1.39193
−2.63515 −38.4420
u = 0.091053 + 0.167445I
a = −3.33529 − 6.24003I
b = 0.244481 − 0.486448I
−0.77407 − 2.77339I −4.75332 − 5.97266I
u = 0.091053 − 0.167445I
a = −3.33529 + 6.24003I
b = 0.244481 + 0.486448I
−0.77407 + 2.77339I −4.75332 + 5.97266I
u = 0.0480242 + 0.1073590I
a = −0.96262 − 6.51872I
b = 0.606334 − 0.040916I
1.33337 − 1.63871I 3.10567 + 5.35613I
u = 0.0480242 − 0.1073590I
a = −0.96262 + 6.51872I
b = 0.606334 + 0.040916I
1.33337 + 1.63871I 3.10567 − 5.35613I
14
II.
I
u
2
= h−1.19×10
16
u
36
−1.98×10
16
u
35
+· · ·+3.73×10
15
b+1.06×10
16
, −7.15×
10
15
u
36
−9.64×10
15
u
35
+· · ·+3.73×10
15
a−3.18×10
16
, u
37
+u
36
+· · ·−8u−1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
11
=
1.91746u
36
+ 2.58688u
35
+ ··· + 33.7288u + 8.53747
3.20312u
36
+ 5.30772u
35
+ ··· − 24.5888u − 2.84598
a
7
=
1.04256u
36
+ 4.09694u
35
+ ··· − 55.3349u − 11.7400
−1.90326u
36
− 1.85536u
35
+ ··· + 12.3168u + 1.70320
a
1
=
u
2
+ 1
u
2
a
10
=
5.12058u
36
+ 7.89460u
35
+ ··· + 9.14006u + 5.69149
3.20312u
36
+ 5.30772u
35
+ ··· − 24.5888u − 2.84598
a
4
=
−0.266371u
36
− 5.46191u
35
+ ··· − 10.7557u + 0.388655
−2.36436u
36
− 2.41065u
35
+ ··· + 1.03658u − 1.72594
a
9
=
−0.200511u
36
− 0.943207u
35
+ ··· + 41.2246u + 2.53862
−1.71820u
36
− 4.55410u
35
+ ··· + 18.6360u + 3.32754
a
8
=
−0.200511u
36
− 0.943207u
35
+ ··· + 41.2246u + 2.53862
−0.572081u
36
− 4.05875u
35
+ ··· + 24.7780u + 4.07023
a
12
=
−0.121535u
36
+ 0.541641u
35
+ ··· + 53.1666u + 7.56314
−0.669721u
36
− 2.37534u
35
+ ··· − 2.31374u + 0.533701
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
37923239655330084
3728078412487259
u
36
−
38434343438741474
3728078412487259
u
35
+···+
122400492787805403
3728078412487259
u+
30710588913013107
3728078412487259
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
37
− 37u
36
+ ··· − 12u + 1
c
2
u
37
+ u
36
+ ··· − 8u − 1
c
3
u
37
− u
36
+ ··· − 6u + 4
c
4
u
37
− 2u
36
+ ··· + u
2
+ 1
c
5
u
37
− u
36
+ ··· − 8u + 1
c
6
u
37
− 7u
36
+ ··· − 253u + 41
c
7
u
37
+ 2u
36
+ ··· − 224u − 23
c
8
u
37
− u
36
+ ··· + 3u + 1
c
9
u
37
− 18u
36
+ ··· + 15u − 1
c
10
u
37
+ u
36
+ ··· − 6u − 4
c
11
u
37
+ 3u
36
+ ··· − 7u + 1
c
12
u
37
− 10u
35
+ ··· − 12u + 4
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
− 47y
36
+ ··· − 1240y −1
c
2
, c
5
y
37
+ 37y
36
+ ··· − 12y −1
c
3
, c
10
y
37
+ 29y
36
+ ··· − 164y −16
c
4
y
37
+ 12y
36
+ ··· − 2y −1
c
6
y
37
− 27y
36
+ ··· − 148617y −1681
c
7
y
37
− 2y
36
+ ··· + 28740y −529
c
8
y
37
+ 17y
36
+ ··· − 5y −1
c
9
y
37
− 18y
36
+ ··· + 15y −1
c
11
y
37
− y
36
+ ··· + 37y −1
c
12
y
37
− 20y
36
+ ··· + 248y −16
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.338592 + 0.948860I
a = 0.95168 − 1.83322I
b = 0.265936 + 0.997961I
3.86482 − 4.14135I 4.53105 + 3.04755I
u = 0.338592 − 0.948860I
a = 0.95168 + 1.83322I
b = 0.265936 − 0.997961I
3.86482 + 4.14135I 4.53105 − 3.04755I
u = 0.265057 + 0.991414I
a = 0.14714 + 2.27315I
b = −0.238262 + 1.085470I
3.72363 + 6.48494I 5.58596 − 8.59239I
u = 0.265057 − 0.991414I
a = 0.14714 − 2.27315I
b = −0.238262 − 1.085470I
3.72363 − 6.48494I 5.58596 + 8.59239I
u = 0.231695 + 1.053600I
a = −0.328847 + 0.338447I
b = 0.13679 − 1.41355I
5.02855 + 5.83791I 2.12557 − 10.81625I
u = 0.231695 − 1.053600I
a = −0.328847 − 0.338447I
b = 0.13679 + 1.41355I
5.02855 − 5.83791I 2.12557 + 10.81625I
u = −0.504429 + 0.758589I
a = 0.559317 − 1.148640I
b = −0.737197 − 0.134602I
1.270810 + 0.262848I 2.31162 − 0.46763I
u = −0.504429 − 0.758589I
a = 0.559317 + 1.148640I
b = −0.737197 + 0.134602I
1.270810 − 0.262848I 2.31162 + 0.46763I
u = 0.249444 + 0.875212I
a = −0.021257 + 0.483417I
b = −0.27473 − 1.39700I
5.68845 − 3.92908I 6.71923 − 2.63498I
u = 0.249444 − 0.875212I
a = −0.021257 − 0.483417I
b = −0.27473 + 1.39700I
5.68845 + 3.92908I 6.71923 + 2.63498I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500516 + 1.000950I
a = 0.062067 − 0.430630I
b = 0.337894 − 0.143349I
0.32441 − 4.22499I −2.12351 + 6.06500I
u = −0.500516 − 1.000950I
a = 0.062067 + 0.430630I
b = 0.337894 + 0.143349I
0.32441 + 4.22499I −2.12351 − 6.06500I
u = −0.244376 + 1.096530I
a = −0.27055 − 1.92483I
b = −0.323355 + 1.155810I
3.72196 − 3.98898I 5.38613 + 4.17982I
u = −0.244376 − 1.096530I
a = −0.27055 + 1.92483I
b = −0.323355 − 1.155810I
3.72196 + 3.98898I 5.38613 − 4.17982I
u = −0.242362 + 0.837304I
a = 0.55946 + 1.62396I
b = 0.190027 + 1.190510I
4.70330 + 2.04272I 4.49829 − 0.65248I
u = −0.242362 − 0.837304I
a = 0.55946 − 1.62396I
b = 0.190027 − 1.190510I
4.70330 − 2.04272I 4.49829 + 0.65248I
u = 0.645588 + 0.949229I
a = −0.342734 + 0.071468I
b = −0.077111 − 1.181410I
6.43211 + 2.47921I 10.05169 + 1.00369I
u = 0.645588 − 0.949229I
a = −0.342734 − 0.071468I
b = −0.077111 + 1.181410I
6.43211 − 2.47921I 10.05169 − 1.00369I
u = −0.946846 + 0.848293I
a = 0.291766 − 0.264862I
b = −0.156013 − 0.757712I
4.74806 − 3.40411I −13.02147 + 0.I
u = −0.946846 − 0.848293I
a = 0.291766 + 0.264862I
b = −0.156013 + 0.757712I
4.74806 + 3.40411I −13.02147 + 0.I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860354 + 0.946621I
a = 1.02362 + 1.62425I
b = −0.11292 + 1.61129I
8.07656 + 3.17381I 22.1999 + 33.1535I
u = 0.860354 − 0.946621I
a = 1.02362 − 1.62425I
b = −0.11292 − 1.61129I
8.07656 − 3.17381I 22.1999 − 33.1535I
u = −0.14840 + 1.48072I
a = −1.283810 + 0.166064I
b = 0.596153 + 0.750938I
−5.26789 + 1.08040I 0
u = −0.14840 − 1.48072I
a = −1.283810 − 0.166064I
b = 0.596153 − 0.750938I
−5.26789 − 1.08040I 0
u = 0.13422 + 1.49054I
a = −1.70068 − 0.10708I
b = 1.44159 − 0.39456I
−7.97369 + 1.95650I 0
u = 0.13422 − 1.49054I
a = −1.70068 + 0.10708I
b = 1.44159 + 0.39456I
−7.97369 − 1.95650I 0
u = −0.402019 + 0.253719I
a = −2.24388 + 1.02418I
b = −0.097540 + 0.470442I
−0.59112 − 3.13623I 3.97798 + 11.06924I
u = −0.402019 − 0.253719I
a = −2.24388 − 1.02418I
b = −0.097540 − 0.470442I
−0.59112 + 3.13623I 3.97798 − 11.06924I
u = −0.02709 + 1.55003I
a = −0.472545 − 0.149266I
b = 0.21990 − 1.49062I
−2.55911 + 4.29661I 0
u = −0.02709 − 1.55003I
a = −0.472545 + 0.149266I
b = 0.21990 + 1.49062I
−2.55911 − 4.29661I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12162 + 1.57920I
a = −1.144380 − 0.532298I
b = 0.726709 + 1.116120I
−3.86937 − 6.23166I 0
u = −0.12162 − 1.57920I
a = −1.144380 + 0.532298I
b = 0.726709 − 1.116120I
−3.86937 + 6.23166I 0
u = 0.391589
a = −0.512068
b = −1.43649
−2.53138 39.2220
u = −0.15033 + 1.63038I
a = 1.021040 + 0.443826I
b = −0.374995 − 0.554817I
−7.70403 − 5.49447I 0
u = −0.15033 − 1.63038I
a = 1.021040 − 0.443826I
b = −0.374995 + 0.554817I
−7.70403 + 5.49447I 0
u = −0.132749 + 0.147531I
a = 3.94862 + 2.70843I
b = −0.304624 − 1.284310I
3.03239 − 5.03709I 5.57732 + 5.98806I
u = −0.132749 − 0.147531I
a = 3.94862 − 2.70843I
b = −0.304624 + 1.284310I
3.03239 + 5.03709I 5.57732 − 5.98806I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
37
− 37u
36
+ ··· − 12u + 1)(u
99
+ 106u
98
+ ··· − 170255u − 961)
c
2
(u
37
+ u
36
+ ··· − 8u − 1)(u
99
+ 53u
97
+ ··· − 259u + 31)
c
3
(u
37
− u
36
+ ··· − 6u + 4)(u
99
+ 27u
97
+ ··· − 45156u + 28964)
c
4
(u
37
− 2u
36
+ ··· + u
2
+ 1)(u
99
+ 3u
98
+ ··· + 29u + 1)
c
5
(u
37
− u
36
+ ··· − 8u + 1)(u
99
+ 53u
97
+ ··· − 259u + 31)
c
6
(u
37
− 7u
36
+ ··· − 253u + 41)
· (u
99
− 8u
98
+ ··· + 11559416u + 409289)
c
7
(u
37
+ 2u
36
+ ··· − 224u − 23)(u
99
+ u
98
+ ··· + 263227u + 47969)
c
8
(u
37
− u
36
+ ··· + 3u + 1)(u
99
+ 2u
98
+ ··· − 5274u − 59)
c
9
(u
37
− 18u
36
+ ··· + 15u − 1)(u
99
− 9u
98
+ ··· − 402u − 215)
c
10
(u
37
+ u
36
+ ··· − 6u − 4)(u
99
+ 27u
97
+ ··· − 45156u + 28964)
c
11
(u
37
+ 3u
36
+ ··· − 7u + 1)(u
99
− 6u
98
+ ··· − 12984u + 3173)
c
12
(u
37
− 10u
35
+ ··· − 12u + 4)
· (u
99
− u
98
+ ··· + 11196996u + 1212452)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
37
− 47y
36
+ ··· − 1240y −1)
· (y
99
− 198y
98
+ ··· − 1536870623y −923521)
c
2
, c
5
(y
37
+ 37y
36
+ ··· − 12y −1)(y
99
+ 106y
98
+ ··· − 170255y −961)
c
3
, c
10
(y
37
+ 29y
36
+ ··· − 164y −16)
· (y
99
+ 54y
98
+ ··· − 26392577344y −838913296)
c
4
(y
37
+ 12y
36
+ ··· − 2y −1)(y
99
+ 21y
98
+ ··· + 287y −1)
c
6
(y
37
− 27y
36
+ ··· − 148617y −1681)
· (y
99
+ 14y
98
+ ··· + 14727329603844y −167517485521)
c
7
(y
37
− 2y
36
+ ··· + 28740y −529)
· (y
99
− y
98
+ ··· + 66159723473y −2301024961)
c
8
(y
37
+ 17y
36
+ ··· − 5y −1)(y
99
− 14y
98
+ ··· + 8482664y −3481)
c
9
(y
37
− 18y
36
+ ··· + 15y −1)(y
99
− 37y
98
+ ··· + 769624y −46225)
c
11
(y
37
− y
36
+ ··· + 37y −1)
· (y
99
− 20y
98
+ ··· − 584095766y −10067929)
c
12
(y
37
− 20y
36
+ ··· + 248y −16)
· (y
99
+ 5y
98
+ ··· + 5946396266144y −1470039852304)
25
